Four poplars

Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be?

Correct answer:

n =  17
x =  7 m

Step-by-step explanation:

$$\begin{gathered} 35=5\cdot 7 \\ 14=2\cdot 7 \\ 91=7\cdot 13 \\ \text{GCD}(35,14,91)=7 \\ x=GCD(35,14,91)=7\text{ m } \\ s=35+14+91=140\text{ m } \\ n=s\mathrm{/}x-3=140\mathrm{/}7-3=17 \end{gathered}$$

$x=7=7\text{ m}$

Try another example

Related math problems and questions:

• Trees in alley
  There are four trees in the alley between which the distances are 35m, 15m and 95m. Trees must be laid in the spaces so that the distance is the same and the maximum. How many trees will they put in and what will be the distance between them?
• Garden
  The garden has the shape of a rectangle measuring 19m²⁰cm and 21m60cm. Mr. Novák will fence it. It wants the distance between adjacent pillars to be at least two meters and a maximum of three meters. He would also like the distances between the adjacent p
• Lcm = 22 + gcd
  The least common multiple of two numbers is 22 more than their greatest common divisor. Find these numbers.
• Gcd and lcm
  Calculate the greatest common divisor and the least common multiple of numbers. a) 16 and 18 b) 24 and 22 c) 45 and 60 d) 36 and 30
• Lamps on playground
  The playground has the shape of a rectangle 36 x 50m. After how many meters will he place the lamps on his lighting, if the distances between them are to be the same on both sides if the builders want to use the smallest possible number of lamps?
• Coloured numbers
  Mussel wrote four different natural numbers with coloured markers: red, blue, green and yellow. When the red number divides by blue, it gets the green number as an incomplete proportion, and yellow represents the remainder after this division. When it div
• 9.A
  9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5?
• Blades
  1st blade 2,5 m, 2nd blade. .1.75 m. How many same long pieces of this two blades can be do the biggest? How long is one piece?
• On Children's
  On Children's Day, the organizers bought 252 chewing gums, 396 candies and 108 lollipops. They want to make as many of the same packages as possible. Advise them what to put in each package and how many packages they can make this way.
• Hectares
  The tractor plows the first day of 4.5 ha, the second day 6.3 ha, and the third day of 5.4 ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is i
• Around the flowerbed
  Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses found in every corner of the flowerbed and consumed them as little as possible. a) At what distance are planted roses? b) How many ros
• Paving - joints
  We are paving with rectangular pavement 18 cm × 24 cm was placed side by side in height in a row and in the second row in width etc. How many times will the joints meet at a distance 10 m?
• Bricks pyramid
  How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
• Apples and pears
  Mom divided 24 apples and 15 pears to children. Each child received the same number of apples and pears - same number as his siblings. How many apples (j=?) and pears (h=?) received each child?
• The tickets
  The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
• We bought
  We bought 140 fruit, 196 chocolate and 84 caramel lollipops. How many of the same packages can we prepare from them?
• MO C–I–1 2018
  An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.